In order to manufacture a packaged device, a die having a sensitive region is bonded to a support, and a packaging mass of moldable material is molded on the support so as to surround the die. During molding of the packaging mass, a chamber is formed, which faces the sensitive region and is connected to the outside environment. To this end, a sacrificial mass of material that may evaporate/sublimate is dispensed on the sensitive region; the packaging mass is molded on the sacrificial mass; a through hole is formed in the packaging mass to extend as far as the sacrificial mass; the sacrificial mass is evaporated/sublimated through the hole.